%link
\begin{lstlisting}
sage: (e*d).mod(p-1)
1
sage: (e*d).mod(q-1)
1
sage: n = p*q
sage: m = random_prime(n)
sage: c = m.powermod(e,n)
sage: m == c.powermod(d,n)
True
sage: m == m.powermod(e*d,n)
True
\end{lstlisting}%link
